Here are my FTL protips (buyer beware, I've died horribly on the seventh wave every single time so maybe I'm not the right guy for the Protip job). Having said that:
1) Comb as much of the first map as possible, because you won't be able to hang about on later sections of the game. At this point, the enemy ships chasing you are fairly weak and you can afford to get caught by them once or twice as you forage near the exit.
2) For the first few levels, passing through a red area isn't quite as bad as it seems. It's worth passing through them if taking the "safer" route means you'll end up in a bunch of nebula sections which almost always mean instadeath later on in the game.
3) When upgrading the ship, a lot of players start powering down the medbay because other bits of the ship need to be up and running (you know, like oxygen and guns or whatever). Don't neglect the medbay! It'll stop you getting dead (important) and you can also use it to fend off ship invasions. How? PULL UP A CHAIR, but first: the doors.
4) Upgrade the doors as soon as possible. On later stages your ship will be on fire pretty much all the time, and if you wander into bug / mantis territory you'll be dealing with ship invasions every couple of hops. Patching up your doors will allow you to deploy some tactics. Position your least favourite redshirt in the vicinity of the invaders (next room over should do it) and shuffle one or two extra guys in the medbay.
Can you see where I'm going with this?
The redshirt will lure the invaders to the medbay where they'll be greeted by three or more shipmates who can lay out a smackdown while being constantly regenerated. There is a downside to this tactic, in the form of the next tip...
5) The moment the invaders look like they're going to die, start filtering your guys out of the medbay asap. The reason for this is the same reason you don't do what I did and get into the habit of healing everybody at once - I lost my entire crew bar one guy when an attacking ship teleported a big explodey thing into the medbay.
Unless you're in a gambling mood (or need to smack up some invaders) then only heal your crew two at a time, max.
6) Always target the enemy weapons, then go for the engines so they can't run away. After that, it's a case of juggling those two and hammering the bridge. I've never really seen any benefit to blasting away at their oxygen supplies.
7) Luck plays a part in this, but when you're on the run and desperately trying to get your hands on supplies, a defence drone will work wonders in fending off attackers long enough to be able to jump to safety. Hands up anybody who ever bothered to use a drone. I'll wait...
8) There is no 8. That's everything, it's all I have. I'll probably remember a few others and update the post but feel free to drop some more in if you have them.